CBCHC8C6CR C8DJDIB2CRBGBCBOA3CTCZBMB0A4BDBRDIBSANCRBGBHDGAXBOC2BRA4 C5B9CNBUBCBOBVLBYAG L = {F i } i∈I ∪{f j } j∈J ∪{c k } k∈K . CBCHC3C5CM C5CM3.15 B2B9CNBUBCBOBVL, N L AXC8DJI DID7ALAXA4BEASCLA5 〈D I , {F i } i∈I , {f j } j∈J , {c k } k∈K 〉 ? D I DIAWBGB9CDBVBQA3AIAGI AXCMBDBTBGABBD,C3BYAG D . ?B2LAXCRBGAHAOACBEBCBOF i ,DCCZAGnBEAX(i ∈ I), F i DIDDAAXAW BGnBEBKAKA3BX F i ? D n ,AIF i AGF i BKI BUAXC8DJA6 ?B2LAXCRBGBNA2ACBEBCBOf j ,DCCZAG m BEAX (j ∈ J), f j DI D DAAX AWBG m BEBNA2A3BX f j : D m → D DIAWBGB2DBA3AIf j AG f j BKI BU AXC8DJA6 ?B2 L AXCRBGBGABAHBEBCBO C k (k ∈ K), c k DI D BUAWBGBEA5A3BX c k ∈ D,AIc k AGc k BKI BUAXC8DJA4 CSCFC3C5CM C5CM3.16 DCI DILAXAWBGC8DJA3D AGI AXCMBDA3N L BKI BUAXAW BGBSCYDIBSD7ALAXBNA2 σ : {x 0 ,x 1 ,x 2 , ···}→D. APDDA3σ(x i ) ∈ D AI AGx i BKBSCY σ ALAXBR (i ∈ N) C5CM 3.18 DCσDIN L BKC8DJIBUAXAWBGBSCYA3x i DIAWBGBGABACBEBCBOA3a ∈ D, σ(x i /a)DIN L BKI BUAXD7ALBSCYA5 σ(x i /a)(x j )= braceleftBigg aj= i σ(x j ) j negationslash= i BXA5 σ(x i /a)DIC5σ BUB2 x i BSCYAXBRBFAG a,CZBA x j (j negationslash= i, j ∈ N)AX BRA8ALAFACA4 σ(x i /a)B8AIAG σ AXAWBG x i –BSCYA4 1 CE 3.20 DCL = {F 2 ,f 1 1 ,f 2 2 ,f 2 3 ,c}, B2APLCCAXB7D7ALCJBGC8DJA5 (1) I 1 = 〈N, {F 2 }, {f 1 1 , f 2 2 , f 2 3 }, {c}〉, CZBUA5 NAGBZD4A2BVA6 F 2 AGNDAAXANAYBKAKA3BXA5 F 2 = {<n,n> | n ∈ N} f 1 1 AGNDAAXBRC0BNA2A3BXA5 f 1 1 : N → N, f 1 1 (n)=n +1 (D5 n ∈ N) f 2 2 AGNDAAXC1B6BNA2A3BXA5 f 2 2 : N 2 → N, f 2 2 (<m,n>)=m + n (D5 m, n ∈ N) f 2 3 AGNDAAXAKB6BNA2A3BXA5 f 2 3 : N 2 → N, f 2 3 (<m,n>)=m · n (D5 m, n ∈ N) c AGNBUAXBEA50. (2) I 2 = 〈Q, {F 2 }, {f 1 1 , f 2 2 , f 2 3 }, {c}〉, CZBUA5 QAGB7CFA2BVA6 F 2 AGQDAAXANAYBKAKA6 f 1 1 AGQDAAXC11 BIA6A3BXA5 f 1 1 : Q → Q, f 1 1 (a)=a +1 (D5 a ∈ Q) f 2 2 BB f 2 3 BA?AGQDAAXC1B6BBAKB6BNA2A4 c D6AGQBUAXBEA50. CT: ?AWBGAWC6BCATLCCAXB7B4BGAF?AXC8DJA4 2 CLC3CR DC σ DIN L BK I BUAXAWBGBSCYA3D7ALBLCWB0B0 N L AXAO tBK I BU σ ALAXBR t σ I (C3BYAG t σ ): (1)AU t AGBGABACBEBCBOx i (i ∈ N) DDA3(x i ) σ I = σ(x i ). (2)AG t AGBGABAHBEBCBOc k DDA3(c k ) σ I = c k . (3)AU t AG f m (t 1 ,t 2 , ···,t m ) DDA3t σ I = f m (t σ 1 ,t σ 2 , ···,t σ m ). CE BKCG 3.20BUA3 σ DIN L BK I 1 BUAXD7ALBSCYA5 σ(x i )=i (D5 i ∈ N) BMA5 x σ i = σ(x i )=i(i ∈ N) c σ = c =0 (f 1 1 (x 1 )) σ = f 1 1 (x σ 1 )=f 1 1 (1) = 1 + 1 = 2 ∈ N (f 2 2 (x 1 ,x 2 )) σ = f 2 2 (x σ 1 ,x σ 1 )=x σ 1 + x σ 2 =1+2=3 (f 2 3 (x 1 ,x 2 )) σ = f 3 2 (x σ 1 ,x σ 1 )=x σ 1 · x σ 2 =3 (f 1 1 (f 2 2 (x 1 ,x 4 ))) σ = f 1 1 ((f 2 2 (x 1 ,x 4 )) σ )=f 1 1 (f 2 2 (x σ 1 ,x σ 4 )) =(x σ 1 + x σ 4 )+1=1+4+1=6 B2D5D5AZAOt BWBSCY σ, t σ ∈ D. 3 C7CGC3CR C5CM3.19 DC σ DIN L BKC8DJI BUAXAWBGBSCYA3D7ALBLCWB0B0 N L AXA1BHDGα BK I BUA9 σ COC0A2A5 ?AUαDIBFBXBHDGF n (t 1 ,t 2 , ···,t n )DDA3αBKIBUA9σCOC0AUD0C9 AUF n (t σ 1 ,t σ 2 , ···,t σ n )AJCHA3BXAUD0C9AU<t σ 1 ,t σ 2 , ···,t σ n >∈ F n . ?AUαAG (?β)DDA3αBKI BUA9 σ COC0AUD0C9AUβ BKI BUAFA9σ COC0A4 ?AU α AG (α 1 →α 2 ) DDA3α BKI BUA9 σ COC0AUD0C9AU α 1 BKI BU AFA9σ COC0BTBN α 2 BKI BUA9 σ COC0A4 ?··· ?AU αAG(?x i )β DDA3αBKI BUA9 σ COC0AUD0C9AUB2CRBGa ∈ D I , β BKI BUB1CXA9σ(x i /a) COC0A4 BY α BK I BUA9 σ COC0AG I | σ α, BBBMBYAG I | σ /α. AQB5 (1) I | σ F n (t 1 ,t 2 , ···,t n ) AUD0C9AU <t σ 1 ,t σ 2 , ···,t σ n >∈ F n ; (2) I | σ ?β AUD0C9AU I | σ /β; (3) I | σ α 1 →α 2 AUD0C9AUA5D9I | σ α 1 , BM I | σ α 2 ; (4) I | σ (?x i )β AUD0C9AUA5B2D5AZ a ∈ D, I | σ(x i /a) β . (5) I | σ α ∨ β AUD0C9AU I | σ α BT I | σ β; (6) I | σ α ∧ β AUD0C9AU I | σ α B5D0I | σ β; (7) I | σ α?β AUD0C9AU I | σ α AXAMAUADC4AG I | σ β; (8) I | σ (?x i )β AUD0C9AUA5ARBK a ∈ D, DFAWI | σ(x i /a) β 4 CE 3.21 DCL = {F 2 }. I =< N,{R},?,? > DILAXAWBGC8DJA3CZBU R = {<a,a>|a ∈ N}. a 1 ,a 2 , ···,a n , ···AGDBUBEA5AXASCLA3COC0A5a 0 = a 1 = a 2 negationslash= a 3 . σ DIN L BK I BUAXD7ALBSCYA5 σ(x i )=a i (D5 i ∈ N). AU α AGK L BUALCLBHDGDDA3 I | σ α AJCHBBBBA7 (1) F 2 (x 1 ,x 2 ); (2) F 2 (x 2 ,x 3 ); (3) F 2 (x 1 ,x 2 )→F 2 (x 2 ,x 3 ); (4) ?x 1 F 2 (x 1 ,x 2 ); (5) ?x 1 ?x 2 F(x 1 ,x 2 ). C8A5 (1) I | σ F 2 (x 1 ,x 2 )AUD0C9AU<x σ 1 ,x σ 2 >∈ F 2 AUD0C9AU<a 1 ,a 2 >∈ R. B6B9a 1 = a 2 , BJ <a 1 ,a 2 >∈ R, AQB5I | σ F 2 (x 1 ,x 2 ). (2) I | σ F 2 (x 2 ,x 3 )AUD0C9AU<x σ 2 ,x σ 3 >∈ F 2 ,AUD0C9AU<a 2 ,a 3 >∈ R. B6B9a 2 negationslash= a 3 , BJ <a 2 ,a 3 >negationslash∈ R, AQB5I | σ /F 2 (x 2 ,x 3 ). (3) I | σ F 2 (x 1 ,x 2 )→F 2 (x 2 ,x 3 )AUD0C9AUI | σ /F 2 (x 1 ,x 2 )BTI | σ F 2 (x 2 ,x 3 ). ATB6 (1)(2)BQA5 I | σ /F 2 (x 1 ,x 2 )→F 2 (x 2 ,x 3 ). (4) I | σ ?x 1 F 2 (x 1 ,x 2 ) AUD0C9AUA5D5AZ a ∈ D, I | σ(x 1 /a) F 2 (x 1 ,x 2 ). AUD0C9AUA5D5AZ a ∈ D, <x σ(x 1 /a) 1 ,x σ(x 1 /a) 2 >∈ F 2 . AUD0C9AUA5D5AZ a ∈ D, <a, a 2 >∈ R. AT a 3 ∈ D, < a 3 ,a 2 >negationslash∈ R. AQB5 I | σ / ?x 1 F 2 (x 1 ,x 2 ). 5 (5) I | σ ?x 1 ?x 2 F 2 (x 1 ,x 2 ) AUD0C9AUA5D5AZ a ∈ D, I | σ(x 1 /a) ?x 2 F 2 (x 1 ,x 2 ). AUD0C9AUA5D5AZ a ∈ D, ARBK b ∈ D, DFAWA5 I | σ(x 1 /a)(x 2 /b) F 2 (x 1 ,x 2 ). AUD0C9AUA5D5AZ a ∈ D, ARBK b ∈ D, DFAWA5 <a, b>∈ R. C1BRAWBGADC4DIAJCHAXA3B1AGBTAUD3 b = a BXCCA4 BJ I | σ ?x 1 ?x 2 F 2 (x 1 ,x 2 ). CE 3.22 LBB I 1 D7CG3.20, σ AGLBK I 1 BUAXD5AWBGBSCYA4AI σ BK I 1 BUDIBB COC0ALCSAXBHDG β: ?x 1 ?x 2 ((?x 3 F 2 (f 2 3 (x 1 ,x 3 ),x 2 ) ∧?x 4 F 2 (f 2 3 (x 2 ,x 4 ),x 1 )) → F 2 (x 1 ,x 2 )) C2A5I 1 | σ β ?B2D5AZ m 1 ∈ N, I 1 | σ(x 1 /m 1 ) ?x 2 ((?x 3 F 2 (f 2 3 (x 1 ,x 3 ),x 2 ) ∧?x 4 F 2 (f 2 3 (x 2 ,x 4 ),x 1 )) → F 2 (x 1 ,x 2 )). ?B2D5AZAX m 1 ∈ N, m 2 ∈ N, I 1 | σ(x 1 /m 1 )(x 2 /m 2 ) (?x 3 F 2 (f 2 3 (x 1 ,x 3 ),x 2 )∧?x 4 F 2 (f 2 3 (x 2 ,x 4 ),x 1 ))→ F 2 (x 1 ,x 2 ). ?B2D5AZ m 1 ,m 2 ∈ N, D9 I 1 | σ(x 1 /m 1 )(x 2 /m 2 ) ?x 3 F 2 (f 2 3 (x 1 ,x 3 ),x 2 ) ∧?x 4 F 2 (f 2 3 (x 2 ,x 4 ),x 1 ), BM I 1 | σ(x 1 /m 1 )(x 2 /m 2 ) F 2 (x 1 ,x 2 ). 6 ?B2D5AZ m 1 ,m 2 ∈ N, D9 I 1 | σ(x 1 /m 1 )(x 2 /m 2 ) ?x 3 F 2 (f 2 3 (x 1 ,x 3 ),x 2 ), D0 I 1 | σ(x 1 /m 1 )(x 2 /m 2 ) ?x 4 F 2 (f 2 3 (x 2 ,x 4 ),x 1 ), BM I 1 | σ(x 1 /m 1 )(x 2 /m 2 ) F 2 (x 1 ,x 2 ). ?B2D5AZ m 1 ,m 2 ∈ N, D9ARBK m 3 ∈ N DFAW I 1 | σ(x 1 /m 1 )(x 2 /m 2 )(x 3 /m 3 ) F 2 (f 2 3 (x 1 ,x 3 ),x 2 ), D0ARBK m 4 ∈ N DFAW I 1 | σ(x 1 /m 1 )(x 2 /m 2 )(x 4 /m 4 ) F 2 (f 2 3 (x 2 ,x 4 ),x 1 ), BM I 1 | σ(x 1 /m 1 )(x 2 /m 2 ) F 2 (x 1 ,x 2 ). ?B2D5AZ m 1 ,m 2 ∈ N, D9ARBK m 3 ∈ N DFAWm 1 · m 3 = m 2 , D0ARBK m 4 ∈ N DFAWm 2 · m 4 = m 1 , BM m 1 = m 2 . ?B2D5AZ m 1 ,m 2 ∈ N, D9 m 1 |m 2 , D0 m 2 |m 1 , BM m 1 = m 2 . AQB5I 1 | σ β . CCCIC4, B2LBK I 2 BUAXD5AWBGBSCY σ, I 2 | σ β ? B2D5AZ m 1 ,m 2 ∈ Q, D9ARBK m 3 ∈ Q DFAWm 1 · m 3 = m 2 , D0ARBK m 4 ∈ Q DFAWm 2 · m 4 = m 1 , BM m 1 = m 2 . AQB5I 2 | σ /β 7 C5CD 3.13 DCσ 1 ,σ 2 DIN L BKCZCVBGC8DJI BUAXCJBGBSCYA3t(v 1 ,v 2 , ···,v n ) DIN L AXAWBGAOA3CZBUA5 v 1 ,v 2 , ···,v n DI N L AXBGABACBEBCBOA3 t(v 1 ,v 2 , ···,v n ) BUANAMAXBGABACBEBCBOB1BK v 1 ,v 2 , ···,v n BUA3 D9B2D5AZ i :1≤ i ≤ n, σ 1 (v i )=σ 2 (v i ),BM t σ 1 = t σ 2 . CQA5B2 t AXBEBJARBLCWBPCTA3BXB2tBUA7BMAXBNA2ACBEBCBOAXBGA2 d CAAQBLCWBPCTA4 (1)AU d =0DDA3t AGBGABACBEBCBOBTBGABAHBEBCBOA4 (1.1)D9 t AGBGABACBEBCBOA3BM t ABAG v 1 ,v 2 , ···,v n BUAXCVAW BGA3AFB7DC t = v i (CV i :1≤ i ≤ n),BMA5 t σ 1 = v σ 1 i = σ 1 (v i )=σ 2 (v i )=v σ 2 i = t σ 2 (1.2)D9tAGBGABACBEBCBOcDDA3BMA5 t σ 1 = c σ 1 = c = c σ 2 = t σ 2 . (2)C2DCd<lDDCUAAAJCHA3CBAG d = l DDD1AP (l>0). DC t BUBMB7 l BGBNA2ACBEBCBOA3 t = f m (t 1 ,t 2 , ···,t m ), CZ BUA5 f m DILBUAXAWBG mBEBNA2ACBEBCBOA3t 1 ,t 2 , ···,t m DI N L AXAOA3B6BLCWC2DCAWA5 t σ 1 1 = t σ 2 1 , t σ 1 2 = t σ 2 2 , ···, t σ 1 m = t σ 2 m , AQB5 t σ 1 = f m (t σ 1 1 ,t σ 1 2 , ···,t σ 1 m )=f m (t σ 2 1 ,t σ 2 2 , ···,t σ 2 m )=t σ 2 . BLCWBPAFA3CUAAAJCHA4 B0CF3.13 A3CTA5AO t(v 1 ,v 2 , ···,v n ) BKBSCY σ ALAXBR t σ BTBB σ B2 t BUANAMAXBGABACBEBCBO v 1 ,v 2 , ···,v n BSCYAXBRB7BKA3BB σ B2CZA8BGABACBEBCBOBSCYAXBRAJBKA4 8 C5CD 3.14 DCσ 1 ,σ 2 DIN L BKCZCVBGC8DJI BUAXCJBGBSCYA3α(v 1 ,v 2 , ···,v n ) DIN L AXAWBGBHDGA3CZBUA5v 1 ,v 2 , ···,v n DIN L AXBGABACBEBCBOA3 α(v 1 ,v 2 , ···,v n )AXBZB6ACBEBCBOB1BK v 1 ,v 2 , ···,v n BUA3D9B2D5 AZ i :1≤ i ≤ n, σ 1 (v i )=σ 2 (v i ),BM I | σ 1 α AUD0C9AUI | σ 2 α CQA5B2BHDGα BUA7BMAXCIC7AOBBCKAOAXBGA2 d CAAQBLCWBPCTA4 (1) AU d =0DDA3α AGBFBXBHDGA3DC α AG F n (t 1 ,t 2 , ···,t n ), CZBUA5 F n AGLAXAWBG n BEAHAOACBEBCBOA3t 1 ,t 2 , ···,t n DIN L AXAOA4B6B9α BUCQB7CKAOA3BMBKt i BUANAMAXCRBGBGABACBEBCBOB1DI α AXBZB6ACBE (1 ≤ i ≤ n), AQB5BK t i BUANAMAXCRBGBGABACBEBCBOBK σ 1 BB σ 2 ALAXBSCYAXBRANAYA3B6B0CF3.13BQA5B2D5AZ i :1≤ i ≤ n, t σ 1 i = t σ 2 i . AQB5I | σ 1 α AUD0C9AU I | σ 1 F n (t 1 ,t 2 , ···,t n ), AUD0C9AU <t σ 1 1 ,t σ 1 2 , ···,t σ 1 n >∈ F n , AUD0C9AU <t σ 2 1 ,t σ 2 2 , ···,t σ 2 n >∈ F n , AUD0C9AU I | σ 2 F n (t 1 ,t 2 , ···,t n ), AUD0C9AU I | σ 2 ‘ α. (2) C2DCCUAAB2A7B7COC0 d<lAX d AJCHA3CBAG d = l DDD1AP (l ≥ 1). (2.1)AUαAG(?β)DDA3B6BLCWC2DCBQA5I | σ 1 βAUD0C9AUI | σ 2 β. AQB5I | σ 1 α AUD0C9AUI | σ 1 ?β AUD0C9AUI | σ 1 /β AUD0C9AUI | σ 2 /β AUD0C9AUI | σ 2 ?β AUD0C9AUI | σ 2 α. 9 (2.2)AU α AG (α 1 →α 2 ) DDA3B6BLCWC2DCBQA5 I | σ 1 α 1 AUD0C9AUI | σ 2 α 1 , I | σ 1 α 2 AUD0C9AUI | σ 2 α 2 . AQB5I | σ 1 α AUD0C9AUI | σ 1 α 1 →α 2 AUD0C9AUI | σ 1 /α 1 BT I | σ 1 α 2 AUD0C9AUI | σ 2 /α 1 BT I | σ 2 α 2 AUD0C9AUI | σ 2 α 1 →α 2 AUD0C9AUI | σ 2 α. (2.3)AUαAG(?v 0 )β DDA3CZBU v 0 AGLAXAWBGBGABACBEBCBOA4B6 B9α AXBZB6ACBEBCBOB1BK v 1 ,v 2 , ···,v n BUA3BJ β AXBZB6ACBEBCBO B1BK v 0 ,v 1 ,v 2 , ···,v n BUA4 BWAZAVA5σ 1 (v 0 /a)(v i )=σ 2 (v 0 /a)(v i )(B2D5AZAXi :0≤ i ≤ n). B6BLCWC2DCAWA5 I | σ 1 (v 0 /a) β AUD0C9AU I | σ 2 (v 0 /a) β, AQB5I | σ 1 α AUD0C9AUI | σ 1 ?v 0 β. AUD0C9AUA5B2D5AZ a ∈ D, I | σ 1 (v 0 /a) β. AUD0C9AUA5B2D5AZ a ∈ D, I | σ 2 (v 0 /a) β. AUD0C9AUI | σ 2 ?v 0 β. AUD0C9AUI | σ 2 α. BLCWBPAFA3CUAAAJCHA4 B0CF3.14DIA3A5B2BHDGα(v 1 ,v 2 , ···,v n )CEA3A3“ I | σ α ”AJ CHBBBBBTBBσ B2αAXCXCVCUCWv 1 ,v 2 , ···,v n BSCYAXBRB7BKA3BB σ B2CZA8BGABACBEBCBOBSCYAXBRAJBKA3 10 CJC9C5CD CNCD DC s, x i BP t BA?DIN L BUAXAOA0BGABACBEBCBOBPAOA4 s prime DIC5s BU A7B7x i BSAGtA7AWAXAOA4σ AGN L BKCZCVBGC8DJI BUAXAWBGBSCYA3 σ prime = σ(x i /t σ ). BM s σ prime =(s prime ) σ . s σ prime : ··· σ prime (x i ) ··· ··· σ prime (x i ) ··· ↓↓ s :(··· x i ··· ··· x i ··· ) s prime :(··· t ··· ··· t ··· ) ↑↑ (s prime ) σ : ··· t σ ··· ··· t σ ··· CQA5B2 s AXBEBJARBLCWBPCTA5 s σ prime =(s prime ) σ (?) (1)AU sAGBGABACBEBCBODDA4 (1.1)D9 s AG x i , BM s prime AG t,AQB5s σ prime = σ prime (x i )=t σ =(s prime ) σ . (1.2) D9 s AGBGABACBEBCBO x j (j negationslash= i), BM s prime AVAG x j , AQB5 s σ prime = σ prime (x j )=σ(x j )=(s prime ) σ . (1.3)D9sAGBGABACAHBEBCBOc,BMs prime AVAGc,AQB5s σ prime = c =(s prime ) σ . (2)D9 s DIAPD7 f m (s 1 ,s 2 , ···,s m ) AXAOA3CZBUA5 f m DILAX AWBG m BEBNA2ACBEBCBOA3s 1 ,s 2 , ···,s m DIN L BUAOA4AX s prime j BYA5 C5 s j BUA7B7 x i BSAG t AWAVAXAO (D5 j :1≤ j ≤ m). BMA5 s prime = f m (s prime 1 ,s prime 2 , ···,s prime m ). B6BLCWC2DCBQA5s σ prime j =(s prime j ) σ (1 ≤ j ≤ m),BMA5 s σ prime = f m (s σ prime 1 ,s σ prime 2 , ···,s σ prime m )=f m ((s prime 1 ) σ , (s prime 2 ) σ , ···, (s prime m ) σ )=(s prime ) σ . BLCWBPAAA3(?) AJCHA4 11 C5CD 3.15 DC α, x i BP t BA?DIN L BUAXBHDGA0BGABACBEBCBOBPAOA3 t B2 x i BK αBUBZB6A4σ AGN L BKCZCVBGC8DJI BUAXAWBGBSCYA3σ prime = σ(x i /t σ ), α prime = α(x i /t). BM I | σ α prime AUD0C9AUI | σ prime α. I | σ prime α : ··· σ prime (x i ) ··· (AJBK) ··· σ prime (x i ) ··· ↓ (BYB5) ↓ (BGA0) ↓ (BYB5) α :(··· x i ··· x i ··· x i ···) α prime :(··· t ··· x i ··· t ···) ↑↑↑ I | σ α prime : ··· t σ ··· (AJBK) ··· t σ ··· CQA5ALB2 α BLCWBPCTA5B2LBK I BUAXD5AZBSCY σ, I | σ α(x i /t) AUD0C9AU I | σ prime α.(??) (1) AU α DIBFBXBHDG F n (s 1 ,s 2 , ···,s n ) DDA3AX s prime j BYC5 s j BUA7B7 x i BSAG t AWAVAXAO (D5 j :1≤ j ≤ n). BM α(x i /t)= F n (s prime 1 ,s prime 2 , ···,s prime n ). B6 (?) BQ s σ prime j =(s prime j ) σ (D5 j :1≤ j ≤ n). AQ B5 I | σ prime α? <s σ prime 1 ,s σ prime 2 , ···,s σ prime n >∈ F n ? <(s prime 1 ) σ , (s prime 2 ) σ ,···, (s prime n ) σ > ∈ F n ? I | σ F n (s prime 1 ,s prime 2 , ···,s prime n )? I | σ α(x i /t). (2)AUαAG(?β)DDA3α(x i /t)AG(?β)(x i /t),BXAG?(β(x i /t)). B6BLCWC2DCBQ I | σ prime β AUD0C9AUI | σ β(x i /t). AQB5I | σ prime /βAUD0C9 AU I | σ /β(x i /t), BX I | σ prime ?β AUD0C9AU I | σ ?β(x i /t), BJ I | σ prime α AUD0C9AUI | σ α(x i /t). (3)AUαAGα 1 →α 2 DDA3α(x i /t)AG α 1 (x i /t)→α 2 (x i /t). B2α 1 BP α 2 DFB4BLCWC2DCAYBP(??) AJCHA4 12 (4)AU α AG (?x j )β DDA4 (4.1)D9i = j,BMA5αBUA7B7x i B1DIBHA1ANAMA3AQB5α(x i /t)=α. B6B9σ BB σ prime B2AFDIx i AXBGABACBEBCBOBSCYAXBRAN?A3B6B0CF 3.14 BQ I | σ α(x i /t) ? I | σ α ? I | σ prime α (4.2)D9 i negationslash= j, BMA5 α(x i /t) AG (?x j )β(x i /t). B6B9t B2 x i BK α BUBZB6A3BJ x i AFBK α BUBZB6ANAMBTBN x j AFBK t BUANAMA4 (4.2.1)D9 x i AFBK α BUBZB6ANAMA3B8 (4.1)CCBP (??) AJCHA4 (4.2.2) D9 x j AFBK t BUANAMA3B6B0CF 3.13 AWA5B2D5AZ a ∈ D, t σ(x j /a) = t σ . AQB5 I | σ α(x i /t) AUD0C9AUI | σ (?x j )β(x i /t), AUD0C9AUA5B2D5AZ a ∈ D, I | σ(x j /a) β(x i /t). AUD0C9AUA5B2D5AZ a ∈ D, I | σ primeprime β(x i /t), σ primeprime = σ(x j /a) AUD0C9AUA5B2D5AZ a ∈ D, I | σ primeprime (x i /t σ primeprime ) β,(BLCWC2DC) AUD0C9AUA5B2D5AZ a ∈ D, I | σ primeprime (x i /t σ ) β, AUD0C9AUA5B2D5AZ a ∈ D, I | σ(x j /a)(x i /t σ ) β. AUD0C9AUA5B2D5AZ a ∈ D, I | σ(x i /t σ )(x j /a) β, (σ(x j /a)(x i /t σ )=σ(x i /t σ )(x j /a)) AUD0C9AUI | σ(x i /t σ ) (?x j )β, AUD0C9AUI | σ(x i /t σ ) α. BLCWBPAFA3 (??)AJCHA4 BPAAA4 13 CPCOCA C5CM3.20DC α AGN L AXAWBGBHDGA3I AGN L AXAWBGC8DJA3 ?D9B2N L BK I BUAXCRBGBSCY σ B1B7 I | σ α, BMAI α BK I BUBOA3 BYAG I |= α. ?D9B2N L BK I BUAXCRBGBSCY σ B1B7 I | σ /α, BMAI α BK I BUC2A4 AX I negationslash|= α ADDHα BK I BUAFBOA4BWAZI negationslash|= α BB α BK IBUC2AXD2?A4 CTA5N L BUCCCXARBKBHDGα, α BK N L AXCVBGC8DJBUBZAFBOAVAFC2A4 C5CD 3.16 DC α, β DIN L AXBHDGA3I DIN L AXC8DJA3BM (1) α BK I BUBO(C2)??α BK I BUC2 (BO) ???α BK I BUBO(C2). (2) α→β BK I BUC2? α BK I BUBOD0 β BK I BUC2A4 CKA5A1 α→β BK I BUBO? α BK I BUC2BTβ BK I BUBOA2AJCHBBBBA7 C5CD 3.17 D9 I |= α, D0 I |= α→β, BM I |= β. C5CD 3.18 I |= α AUD0C9AUI |=(?x i )α. CQA5(?)DCI |= α. AUBPI |=(?x i )α,BTAUBPA5B2N L BKI BUAXD5AW BGBSCY σ, D5AZ a ∈ D, I | σ(x i /a) α. BWAZI |= α BXCCA4 (?) DC I |= ?x i α, ALBP I |= α. B2 N L BK I BUAXD5AWBGBSCY σ, B1 I | σ (?x i )α, BJB2D5AZ a ∈ D, I | σ(x i /a) α. A9?AZA3D3 a 0 = σ(x i ) ∈ D,BM I | σ(x i /a 0 ) α. B5 σ(x i /a 0 )=σ, BJ I | σ α. 14 C5CM 3.21 DC α AGN L AXAWBGBHDGA4 (1)AI α DIB3BODGA3D9 α BK N L AXD5AWBGC8DJBUB1AGBOA3BYAG|= α; (2)AI α AGCPB3DGBTB3C2DGA3D9α BKN L AXD5AWC8DJBUB1AGC2A4 AYBPA5 (1) |= α AUD0C9AUA5B2D5AWC8DJI BWD5AWBSCY σ, I | σ α. (2) α DIB3C2DGAUD0C9AUA5B2D5AWC8DJI BUBWD5AWBSCY σ, I | σ /α. C5CD 3.20 B2N L AXD5AZBHDGα, β. (1) α B3BO(C2) ?? ? α B3C2 (BO); (2) α→β B3C2?? α B3BOD0 β B3C2A6 (3)D9|= α D0|= α→β, BM|= β; (4) |= α ?? |=(?x i )α C5CM3.9 DCαAGNBUBHDGA3C5BKαBUANAMAXA7B7CUAAACBEBCBOp 0 ,p 1 , ···,p n ?DDBA?BSAGLAXBHDGα 0 ,α 1 ,α 2 , ···,α n ,AWAVAXLBUBHDGβ AI AG α BKLBUAXAWBGASD8DECGA4 15 C5CD 3.21 D9α prime DIPBUAXAWBGBVATDGA3BM α prime BKN L BUAXD5AWBGASD8DECGαDI B3BODGA4 CQA5DC α prime BUANAMAXCUAAACBEBCBOB1BK p 0 ,p 1 ,p 2 , ···,p k BUA3α DI C5 α prime BUA7B7p i B1ACBSAGN L BUBHDGα i AWAVAXBHDG (0 ≤ i ≤ k). AU BP α DIB3BODGA3BTAUBPA5B2 N L AXD5AWBGC8DJI BW N L BK I BUAXD5 AWBGBSCY σ, I | σ α, AGAPBIBLPAXAWBGBSCY v D7ALA5 v : {p 0 ,p 1 , ···,p n ,···}?→{0, 1} v(p i )= ? ? ? ? ? ? ? 1 D9 0 ≤ i ≤ k D0 I | σ α i 0 D9 0 ≤ i ≤ k D0 I | σ /α i 0 i>k AXALB2 α prime AXBEBJARBLCWBPCTA5 I | σ α AUD0C9AUv(α prime )=1 (?) (1)AU α prime AGCUAAACBEBCBOp i (CV i :0≤ i ≤ k) DDA3BM α AG α i , AQB5v(α prime )=1?? v(p i )=1?? I | σ α i ?? I | σ α. (2)AUα prime DI?β prime DDA3DCβ AGC5β prime BU p 0 ,p 1 ,p 2 , ···,p k BA?AC BSAG α 0 ,α 1 ,α 2 , ···,α k AWAVAXN L BUAXBHDGA3BM α AG?β. B6BL CWC2DCBQA5 I | σ β AUD0C9AUv(β prime )=1.AQB5 I | σ α ?? I | σ ?β ?? I | σ /β?? v(β prime )=0?? v(?β prime )=1?? v(α prime )=1. (3)AU α prime AG α prime 1 →α prime 2 DDA3B8(2)CCBPA4 BLCWBPAFA3 (?) AJCHA4 AQB5A3B6B9α prime AGPAXBVATDGA3BJv(α prime )=1,A7AXA3 I | σ α. 16